In a 9-inch skillet, melt the butter over medium heat. Add the sugar and cook, stirring, until the syrup is a light caramel color, about 2 minutes.
Add the plantains, tossing to coat, and cook until tender, about 3 minutes. Add the apple juice and boil 1 minute, or until thickened slightly. Stir in the cinnamon and remove from the heat.
Divide the plantains among 4 dessert plates and spoon the juices over each.